Sums of ell-variate ridge functions approximate r-smooth Sobolev functions on R^d at the optimal rate n^{-r/(d-ell)}, giving sharp rates for generalized translation networks and complex-valued neural networks.
Nearly-tight VC-dimension and pseudodimension bounds for piecewise linear neural networks
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On best approximation by multivariate ridge functions with applications to generalized translation networks
Sums of ell-variate ridge functions approximate r-smooth Sobolev functions on R^d at the optimal rate n^{-r/(d-ell)}, giving sharp rates for generalized translation networks and complex-valued neural networks.